The Quantum Group ${{\mathrm{GL}}}_q(2)$

Abstract

In this paper, we fix once and for all a field $\mathbb {K}$. A ring (or an algebra) means an associative $\mathbb {K}$-algebra with unit, not necessarily commutative. It is suggestive to imagine the ring $A$ as a ring of (polynomial) functions on a space which is an object of noncommutative, or “quantum,” geometry. Morphisms of spaces correspond to ring homomorphisms in the opposite direction. For $A$ and $B$ fixed, the set ${{\mathrm{Hom}}}_{\mathbb {K}{-}\mathrm {alg}}(A, B)$ is also called the set of $B$-points of the space defined by $A$.